Question

A function f(x) is defined as under: $f\left(x\right)=\{\begin{array}{cc}x+2& x<1\\ 4x-1& 1\le x<3\\ x^2+5& x>3\end{array}$ Determine $limf\left(x\right)$ when $x\to 1$

Answer 1

L.H.L $=\underset{x\to 1^{-}}{lim}f\left(x\right)=\underset{x\to 1^{-}}{lim}(x+2)=3$
R.H.L $=\underset{x\to 1^{+}}{lim}f\left(x\right)=\underset{x\to 1^{-}}{lim}(4x-1)=3$
Clearly L.H.L$=$R.H.L$=3$ . Hence limit exist and its value is 3.